Error Model for Cat States in Superconducting Kerr Nonlinear Resonators

Quantum error correction protocols require up to thousands of physical qubits per logical qubit in order to protect quantum information from unavoidable errors. A hardware efficient solution is therefore essential for the realization of quantum computers due to the challenge of creating and controlling a high number of qubits. A particularly attractive approach to realize these ideas is using cat states in microwave cavities. I will first summarize a scheme based on two-photon driven Kerr nonlinear resonators for stabilizing cat states [1] and then discuss the error model within this scheme. This model based on photon loss has the interesting property of being biased: photon loss leads to errors close to a ‘bit flip’ error on the cat states subspace while ‘phase flip’ errors are suppressed. Optimizing quantum error correction to take advantage of biased errors has the potential to significantly decrease the number of qubits required by error correction protocols.
[1] S. Puri et al., npj Quantum Information 3, 18 (2017)